6.3.4 Equivalent Ratios

You will notice in the two given scenarios that each of the given ratios are taken down to their unit rate. By doing this, you are making them easier to compare and you can also use this to easily see whether or not the ratios are equivalent (equal) to each other.

In this set of examples, we are simply using multiplication and division to prove whether or not the ratios are equivalent. In the first example, the top is multiplied by 3 to get 9 while the bottom is multiplied only by 2. Since the top and bottom are being multiplied by two different numbers, the two ratios are not equivalent.

In the second example, you will notice that both the top and bottom of the ratio are divided by the same number in order to get the second ratio. Since that is true, the ratios are equivalent.